An old chestnut is back: A party won’t be able to settle on a nominee, and its convention will be deadlocked. Karl Rove, in surveying the 2016 Republican race, is the latest to raise such a prospect.

His take? Five candidates — Ben Carson, Donald Trump, Marco Rubio, Ted Cruz and Jeb Bush — all have “the message, money, organization and poll numbers to play the long game,” and if each one continues to accumulate delegates, the Republican convention in summer 2016 may open without a candidate holding a majority.

True, each of those five could survive past the early contests. But all five?

As convention-rules maven Josh Putnam explains, Rove is fuzzy on how delegates are chosen and apportioned under the current Republican rules. But the main thing Rove is wrong about is the idea that five strong candidates will remain deep into the process.

Suppose, for example, the current polls hold, and Jeb Bush finishes fifth in Iowa and then sixth in New Hampshire. He would likely drop out.

But suppose he pushes through to one more state. Most of what people would be hearing about him would be negative — that he’s a loser. Meanwhile, the winners (or at least those who beat expectations) in Iowa and New Hampshire would benefit from the favorable or at least relatively extensive attention they get afterward.

The Republican Party actors who desperately wanted to stop Ben Carson and Donald Trump would be jumping on the bandwagon of the candidate they thought had the best chance of stopping them. Maybe that person would be Marco Rubio, based on polling right now. Some of Bush’s supporters might jump ship. Behind the scenes, party leaders would be pushing Bush to surrender rather than risk harming the party by continuing to wage an increasingly impossible effort.

If all this came to pass, Bush would likely do badly in South Carolina. And as the pressures on him increased, he wouldn’t continue.

At least, that’s how winnowing has worked for four decades. The losing candidates drop out, and the field of winners gets smaller and smaller.

The exceptions have included factional candidates who have support spread out over many states that will stick with them regardless of the chances of victory, and are interested more in changing the party’s platform than in winning the nomination. Jesse Jackson in 1984 and 1988 and Ron Paul in 2008 and 2012 are examples. There doesn’t appear to be anyone like that in the Republican field this time.

Of course, the “Bush defeated” scenario is only one possible outcome. He could rally and finish well in Iowa, with Rubio faltering and dropping out. Or perhaps Chris Christie or Bobby Jindal will surprise us and surge. Maybe Trump and Carson collapse, and Bush, Rubio and Ted Cruz are the Iowa winners, and those three all make it through South Carolina.

The brutal logic of place-order always holds: If someone does well, someone else does badly. And those who do badly drop out.

The wild card in this cycle was supposed to be the enormous amounts of money collected by candidate-supporting super-PACs. But, as demonstrated by Rick Perry and Scott Walker, that source of funds won’t keep candidates in who would otherwise fold.

So winnowing works. We aren’t going to have 15 candidates in New Hampshire. We aren’t going to have 10 in South Carolina. We aren’t going to have more than five coming out of South Carolina, and more than three are unlikely to survive through March.

It remains far more likely that we will have a clear nominee by the time the results of the South Carolina primary are announced on Feb. 20 than that we have three candidates on fairly even terms at the end of March. Three equal candidates after March is the minimum it would take to deadlock the convention — that is, none of them has 50 percent of the delegates plus 1 by the end of the primaries. It’s not going to happen.

There is no rhyme or reason, and nothing that could pass for a justifiable goal or an ounce of sense, in the infliction of misery on the 800,000 federal employees either on furlough or working without pay.